Micro-tearing mode dominated electron heat transport in DIII-D H-mode pedestal

A new, comprehensive set of evidence reveals that Micro-Tearing Modes (MTMs) dominate pedestal electron heat transport in an H-mode experiment in the DIII-D tokamak. The experiment investigates the role of MTMs by scanning pedestal collisionality, a main drive of MTM instability, from 0.43 to 0.84 on the pedestal top. Broadband (150–800 kHz) magnetic and density fluctuations originating from the pedestal gradient region and highly consistent with MTMs are observed, with amplitude increasing during the scan. The higher magnetic fluctuation amplitude correlates with a lower pedestal electron temperature gradient, implying MTMs may regulate the pedestal electron heat transport. The collisionality scan results in profile and transport changes consistent with predicted transport capability of MTMs: (1) experimentally-determined electron heat diffusivity increases ∼40% at the location where the broadband density fluctuations peak; (2) ion heat diffusivity has less increase (<20%); and (3) a locally flattened region in the electron temperature pedestal is observed at high collisionality. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, local, nonlinear simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. This result establishes MTMs as an effective transport mechanism in the H-mode pedestal, in particular at high collisionality.

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Introduction
Understanding pedestal turbulence and transport is critical for fusion energy. Pedestal is a narrow region with large density, temperature and pressure gradients at the edge of a high confinement (H-) mode tokamak plasma [1]. The pedestal connects plasma core and Scrape-Off-Layer (SOL) and therefore can affect both fusion energy gain and heat exhaust. Plasma transport in the pedestal has been predicted to be regulated by various instabilities [2][3][4][5]. Experimental validation of those predictions is critical to develop solid physics understanding for future fusion devices. Recently, several gyrokinetic simulations have predicted Micro-Tearing Modes (MTMs) play a major role in electron heat transport in the H-mode pedestal [6][7][8][9][10]. Experimentally, magnetic and density fluctuations highly consistent with MTMs have been identified in the JET [8,10] and DIII-D [9,[11][12][13][14][15][16] tokamaks. In addition, some experimental evidence implying MTM-induced pedestal electron heat transport has been reported, including: (1) experimentally-determined ratio of electron heat to particle diffusivity is greater than unity, consistent with MTM-induced transport [7,13]; (2) amplitude of magnetic fluctuations consistent with MTMs correlates with plasma confinement [11,12]; and (3) amplitude of magnetic fluctuations consistent with MTMs correlates with the saturation of pedestal electron temperature gradient between occurrence of Edge-Localized-Modes (ELMs) [12,13]. Nevertheless, experimental evidence supporting that MTMs can dominate pedestal electron heat transport has not been reported. In this paper, a comprehensive set of experiment-based evidence is presented, revealing that MTMs dominate pedestal electron heat transport in an ELMy H-mode experiment in the DIII-D tokamak. The paper is organized as follows: experimental conditions are introduced in section 2; measurements of fluctuations consistent with MTMs are detailed in section 3; inter-ELM temporal evolution of pedestal gradients and fluctuations is presented in section 4; transport analysis is shown in section 5; gyrokinetic simulation results are detailed in section 6.

Experimental conditions
This work focuses on an ELMy H-mode experiment (shot number 183225; figure 1) in the DIII-D tokamak [17]. The experiment has 1 MA total plasma current, −2 T toroidal magnetic field (minus sign corresponds to counter-current direction), and 6 MW auxiliary heating power from neutral-beam injection. The plasma is upper single-null diverted with ion ∇B drift away from the divertor ( figure 1(a)). Elongation, upper and lower triangularity of the plasma are 1.73, 0.49, 0.24, respectively. Increased gas puffing (location indicated by the yellow arrow in figure 1(a)) is applied during the ELMy H-mode to slowly ramp up the plasma density and therefore increase the pedestal collisionality (figures 1(b) and (c)). In this paper, electron collisionality v * e (∝ n e /T 2 e [18]) measured on the pedestal top is used. The experiment is designed based on the following: (1) increased collisions can destabilize MTMs [7] to assess MTM-induced transport, and (2) fluctuations consistent with MTMs have been observed previously in similar plasma discharges [11,12].
A low collisionality window (ν * e = 0.43 ± 0.11, figure 1, blue bar) from 2.7 to 3 s and a high collisionality window (ν * e = 0.84 ± 0.36, figure 1, red bar) from 3.4 to 3.7 s are analyzed. Both windows have type-I ELMs ( figure 1(d)). The ELM repetition frequency is slightly higher at the high collisionality (117 Hz compared to 107 Hz), which does not affect inter-ELM transport analysis, as shown in section 4. The analyzed time window at high collisionality is limited to before 3.7 s, because several changes in edge plasma conditions occur later, including: (1) the ELMs gradually transit from type-I to type-III (figure 1(d)); (2) SOL radiation power begins to increase (figure 1(e)); and (3) the edge plasma starts to detach at 3.8-3.9 s (not shown). These changes would complicate pedestal physics interpretation [19].
Measured (crosshairs) and fitted (solid lines) plasma profiles within 80%-99% of inter-ELM period at the low (blue) and high (red) collisionalities are shown in figure 2. Electron density n e , temperature T e and pressure P e are measured by a Thomson scattering diagnostic [20] and fitted by a hyperbolic tangent function [21] to determine the location and value of pedestal-top (red and blue dashed lines in figure 2). The pedestal-top is located at ψ N = 0.95-0.96, where is the normalized poloidal magnetic flux. Impurity ion (Carbon 6+) density and temperature are measured by a Charge-Exchange Recombination (CER) diagnostic [22] and fitted by the hyperbolic tangent function and a spline function, respectively. Because of uncertainties in the equilibrium reconstruction, alignment of the electron profiles with respect to the separatrix is determined by a two-point model [23]: the profiles are shifted so that the separatrix electron temperature is equal to 80 eV. Impact of this shift on transport and gyrokinetic simulation is investigated in sections 5 and 6, respectively. From the low to high collisionality, the pedestal electron density increases (figure 2(a)) while the electron density gradient is largely unchanged ( figure 2(b)). In contrast, both the pedestal electron temperature and its gradient (figures 2(c) and (d)) decreases dramatically (∼30%), resulting in a decrease in electron pressure and its gradient (figures 1(e) and ( f )). The profile peaking, defined as the ratio of a given plasma parameter at ψ N = 0 and ψ N = 0.9, slightly changes from 4.9 to 5.1 for electron temperature and 1.6-1.4 for electron density from the low to high collisionality conditions, suggesting transport change primarily happens in the pedestal. Following sections present a set of evidence supporting that the lowered pedestal electron temperature gradient is caused by enhanced electron heat transport driven by MTMs.

Fluctuation measurements
A Faraday-effect Radial-Interferometer-Polarimeter (RIP) is used to measure line-averaged magnetic and density fluctuations simultaneously along the midplane (figure 1(a), blue horizontal lines) [24,25]. Localized density fluctuations are also measured by a Beam-Emission-Spectroscopy (BES) diagnostic at the Low-Field-Side (LFS) midplane (figure 1(a), green dots) [26]. Both diagnostics are sensitive to fluctuations with poloidal wave number k θ less than 1 cm −1 . RIP and BES bandwidth is 1 and 0.5 MHz, respectively.
High frequency (∼150-800 kHz), broadband magnetic and density fluctuations are observed by the RIP and BES at the low and high collisionalities (figure 3; ELMs are removed from the data before the calculation for frequency spectrum). These fluctuations have been previously investigated and identified as originating from MTMs [11,12,15]. The following briefly presents key features of these fluctuations; interested readers are invited to look into the [11,12,15] for more detail. The fluctuations of concern are from ∼150 to 800 kHz. Fluctuations below ∼150 kHz (shaded area in figure 3) consist of coherent and broadband features distinctly different from the high frequency part; the low frequency part have been discussed previously [12,27] and are beyond the scope of this paper. The RIP-measured magnetic and density fluctuations are broadly correlated from 150 to 800 kHz, with squared coherence [28] up to 0.45 (figure 3(d)). The high coherence indicates the broadband magnetic and density fluctuations originate from the same instability. In particular, the broadband magnetic fluctuations cause magnetic field line advection, which can drive density fluctuations that vary with density gradient and may explain the different spectral shapes of the magnetic and density fluctuations (figures 3(a) and (b)) [11]. BES measurement at ψ N = 0.975 indicates the broadband density fluctuations are localized in the pedestal (figure 3(c), 150-500 kHz) where density gradient is steepest. The spectral shapes of density fluctuations measured by BES and RIP are not exactly the same; for instance, RIPmeasured density fluctuations are relatively flat from 150 to 300 kHz (figure 3(b)), whereas BES-measured density fluctuations peak around 350 kHz at low collisionality and exhibit a dual-peak structure at high collisionality (figure 3(c)). This is likely attributed to the difference between line-averaged and localized measurements. Because both measurements have similar wave number sensitivity and overlapping spatial coverage at the LFS midplane, it is reasonable to conclude that the density fluctuations measured by BES and RIP in the same frequency range (150-500 kHz) originate from the same instability. This is further supported by the fact that from the low to high collisionality, the density fluctuation amplitude measured by both RIP and BES has an increase for frequencies from 150 to ∼300 kHz and a decrease above ∼300 kHz (figures 3(b) and (c)). Additional supporting evidence can be found elsewhere (e.g. figure 5 in [12]). Therefore, it is concluded the broadband, > ∼ 150 kHz magnetic and density fluctuations measured by RIP and BES all originate from the same instability.
BES provides spatially-resolved density fluctuation measurement important for mode identification. Radial BES channels show that the broadband density fluctuations peak at ψ N = 0.975 ± 0.01 (figure 4(a)), near the location of maximum pedestal temperature gradient (figure 2(d)). Poloidally-separated BES channels measure poloidal wave number k θ as a function of frequency, allowing direct comparison of dispersion relation between the density fluctuations and MTM prediction ( figure 4(b)). The poloidal wave number of broadband density fluctuations ranges from ∼0.3 cm −1 to ∼0.5 cm −1 (solid lines in figure 4(b)). By using plasma parameters at ψ N = 0.975, MTM frequency is calculated as [8] (dashed lines in figure 4(b)), where ω * e is electron drift frequency, ω E×B is E × B Doppler frequency (dotted lines in figure 4(b)), B T is strength of toroidal magnetic field, p e is electron pressure and e is the charge of electron. From the low to high collisionality, the Doppler frequency is largely unchanged while the MTM frequency decreases about 30% due to a reduced ω * e resulting from the lower electron temperature gradient (figure 2(d)). Note that the positive sign of frequency in figure 4(b) corresponds to propagation in the electron diamagnetic direction in the lab frame. The BES-measured frequency and poloidal wave number of density fluctuations agree with that of MTMs within ±10% (shaded area in figure 4(b)) at both the low and high collisionalities, strongly supporting the conclusion that the broadband density fluctuations measured by BES and RIP, and therefore the RIP-measured magnetic fluctuations, originate from MTMs in the pedestal gradient region. To the authors' best knowledge, no other instability can explain the observed high-frequency, broadband magnetic and density fluctuations [11]. Therefore, it is concluded that the high frequency broadband magnetic and density fluctuations originating from the MTM instability.
The broadband magnetic fluctuation amplitude increases from the low to high collisionality, consistent with theory that MTMs can be driven more unstable by increasing collisions [7]. The line-averaged amplitude of magnetic fluctuation [12], integrated from 150 to 800 kHz (figure 3(a)), increases from 3.4 ± 0.4 to 3.9 ±0.5 Gauss. Consistently, the normalized amplitude of density fluctuations at ψ N = 0.975 increases from 0.36 to 0.4%. MTMs can generate electron heat transport scaled as the square of local, radial magnetic fluctuation amplitude δB 2 r [29,30]. Taking the line-averaged magnetic fluctuation amplitude as a rough proxy of δB r in the pedestal, a 32% increase of pedestal electron heat diffusivity from the low to high collisionality is implied. As will be shown later, this largely agrees with the transport analysis in section 5 and supports the claim that MTMs dominate pedestal electron heat transport.

Inter-ELM temporal evolution
Inter-ELM temporal evolution indicates MTMs are important in limiting pedestal electron temperature gradient. Ensemble averaging is necessary to obtain the inter-ELM evolution, because temporal resolution of the Thomson scattering measurement (∼10 ms) is not fast enough to directly resolve the ELM cycle (∼10 ms). Data from shot 183225 and two similar shots 183223 and 183226, in total 193 and 141 ELM cycles at the low and high collisionality condition, respectively, are ensemble-averaged (figure 5). The mean value (solid lines in figure 5) and standard deviation (shaded areas in figure 5) is calculated with 1 ms resolution. An ELM cycle includes an ELM event from t ELM = 0 to ∼2 ms, when the D α signal level is high (figure 5(a) and gray vertical bar in figure 5), and an inter-ELM period from ∼2 to ∼10 ms. Pedestal gradient is calculated as the ratio of fitted pedestal height to width. At the low collisionality, the pedestal electron temperature gradient recovers from 2 to 6 ms and then is nearly saturated from 6-10 ms ( figure 5(b), blue); the electron density gradient has similar temporal growth to the temperature gradient but saturates earlier at t ELM = ∼4 ms ( figure 5(d), blue), consistent with previous observations [12,31,32]. At the high collisionality, however, electron temperature gradient is clamped and nearly recovered after t ELM =2 ms, while the density gradient still increases from 2 to 6 ms. This is a clear indication that temperature and density gradients are regulated by different transport mechanisms. Both gradients saturated far from the next ELM event at ∼10 ms and therefore rule out ELM as a mechanism. MTMs, which are predicted to generate significant electron heat transport but only small particle transport [7], can explain the lower electron temperature gradient. This is supported by the measured broadband magnetic fluctuation amplitude (figure 5(c)), which is higher during the entire inter-ELM phase (2-10 ms) at the high collisionality.

Transport analysis
Pedestal heat transport at the low and high collisionalities is calculated by using the ONETWO transport code [33] and experimental electron and impurity ion profiles measured within 80%-99% of the inter-ELM period (figure 2). The calculation assumes a stationary plasma state, justified by the saturated pedestal gradients after t ELM = 6 ms (figure 5). From the low to high collisionality, the calculated total electron heat flux flowing across the separatrix increases from 1.65 to 2 MW while total ion heat flux decreases from 2 to 1.85 MW. The calculated electron heat diffusivity increases from the low to high collisionality in the pedestal region (ψ N = 0.96-0.99 in figure 6(a)), while ion heat diffusivity has less increase from the pedestal top (ψ N ≈0.96) to the pedestal gradient region (ψ N ≈0.98) ( figure 6(b)). Note that results beyond ψ N >0.99 is probably inaccurate because of the scattered impurity ion data ( figure 2(h)). The transport change is more clearly seen by showing the ratio of heat diffusivity from the high to low collisionality ( figure 7). The ratio of electron heat diffusivity has a maximum at 1.4, that is a 40% electron heat transport increase ( figure 7(a), green), near the peak location of the broadband density fluctuations (ψ N = 0.975). The ratio of ion heat diffusivity in the same location is almost at unity ( figure 7(b), green), indicating negligible change in ion heat transport.
Sensitivity of the transport calculation associated with the ion and electron data is evaluated. Recent research has shown that main ion CER measurement may determine the pedestal ion temperature more accurately and therefore improve pedestal transport calculation [34]. Transport calculation using main ion data has been performed to evaluate sensitivity related to ion data. Notably, the calculation using main ion data (figure 7, blue) also shows a larger electron heat diffusivity increase (up to 60%) and a smaller ion heat diffusivity increase (up to 20%) in the pedestal region (ψ N >∼ 0.96), consistent quantitatively with the results using impurity ion data. Compared to impurity-ion calculation (green), peak location of maximum χ e increase in the main-ion calculation (blue) is slightly shifted inward from ψ N ≈ 0.98 to 0.97, still close to the peak location of the broadband density fluctuations (ψ N = 0.975). Sensitivity associated with electron data, specifically the setting of T e,sep value (section 2), is also evaluated. Different values of T e,sep are used to fit electron profiles and calculate consequent heat diffusivities. When T e,sep is set to 70 or 90 eV at both collisionalities, the χ e change (figure 7, orange and red) is almost the same as the case with T e,sep = 80 eV. A larger χ e increase up to 60% is seen when T e,sep is set 10 eV lower at the high collisionality (figure 7, purple and grey). The different T e,sep values do not change χ i significantly ( figure 7(b)). All the transport calculations consistently show that χ e exhibits a larger increase χ i than near the peak location of the broadband density fluctuations, supporting MTMs as the mechanism for the observed transport change from the low to high collisionality. Note that the maximum χ e increase (40%-60%) largely agrees with the estimated electron heat transport increase (32%) using the measured broadband magnetic fluctuation amplitude in section 3.
Interestingly, transport changes consistent with MTMinduced transport are also directly evidenced in measured electron temperature profile. At high collisionality, the electron temperature exhibits a relatively flat region in ψ N = 0.97 − 0.99 at T e ≈ 300 eV ( figure 2(c), black dashed box, red crosshairs), which is not observed at the low collisionality (blue crosshairs). The flat region coincides with the peak location of the broadband density fluctuations, implying a role of MTMs. The locally flattened region is observed robustly in examined discharges with similar high collisionality conditions ( figure 8). Electron temperature is relatively flat around Z = 0.57 m (Z is the vertical position of the Thomson scattering measurement shown as red dots in figure 2; Z = 0.54-0.58 m corresponds roughly to ψ N = 0.96-1) in all examined high collisionality cases (figure 8(a), red) but not in any of the low collisionality cases ( figure 8(a), blue). Additionally, this flattening in the steep gradient region (Z≈0.57 m) is not observed in electron density data, regardless of low or high collisionality ( figure 8(b)). One might consider density is flattened around Z = 0.55-0.56 m; however, this is already near the pedestal top and away from the steep gradient region, noting the density pedestal is narrower than the temperature pedestal (figures 2(a) and (c)). These observations are highly consistent with prediction of a global nonlinear simulation, in which MTMs flatten the electron temperature but not the electron density pedestal ( figure 17 in [7]).

Gyrokinetic simulation
A local, linear gyrokinetic simulation using the CGYRO code [35] and the experimental profiles (figure 2) finds that MTMs are unstable at both the low and high collisionalities.
The simulation identifies MTM based on eigenfunction structure and dispersion relation [36]. MTMs are found to be the most unstable mode at ψ N = 0.97 and 0.98, where the electron temperature gradient is largest ( figure 9(a)). The maximum MTM growth rate increases from the low to high collisionality, consistent with observed increase of the broadband magnetic fluctuation amplitude ( figure 3(a)). Wave number of the unstable MTMs at ψ N = 0.98 is 0.09-0.16 cm −1 ( figure 9(b)), slightly lower to that of the observed broadband density fluctuations ( figure 4(b)).
Local, nonlinear CGYRO simulations at ψ N = 0.98 also support that MTMs are experimentally-relevant. Convergence of the nonlinear simulation is found sensitive to input profiles: the simulation using the fitted profiles in figure 2 (with T e,sep = 80 eV; case 1 and 2 in table 1) failed to converge, whereas those using another set of fitted profiles with T e,sep = 40 eV (case 3 and 4 in table 1) does converge. Parameters of the different sets of profiles are summarized in table 1. This convergence sensitivity is not fully understood and speculated to be related to slight difference in the kinetic magnetic equilibrium constructed from the fitted profiles. We note that   (table 1) are not far apart, assuming 20% uncertainty in each set of profiles; by performing sensitivity scans, as shown below, we believe simulations using the profiles with T e,sep = 40 eV can provide useful insight relevant to the experiment. In the converged low collisionality case (case 3 in table 1), saturated fluctuations (contour in figure 10(a)) have averaged wave number and frequency (solid black line in figure 10(a)) agreeing with MTM dispersion (dashed black line in figure 10(a)), indicating MTMs dominate in the nonlinear simulation. The MTMs are found in the entire range of simulated wave number, that is k y ρ s up to 0.16, or k θ up to 0.6 cm −1 . This contains and is wider than that of the MTMs in the linear simulation as well as that of the experimental broadband density fluctuations. The simulated total electron heat flux in the converged low and high collisionality cases (case 3 and 4 in table 1) is 7.6 MW and 9.3 MW ( figure 10(b)), respectively, qualitatively consistent with but quantitatively much higher than the experimental value (∼2 MW in section 5). The higher electron heat flux is found to be mainly attributed to the collisionality, the normalized electron temperature gradient (a/L Te ) and magnetic shear (ŝ) in case 3 and 4, all of which are key parameters affecting MTM stability [36]. Increasing the magnetic shear (case 5 in table 1) or reducing the normalized electron temperature gradient (case 6 in table 1) leads to a lower electron heat flux (3-4 MW) closer to the experimental value, as expected for MTM-driven transport. Note that case 1 and 2 have a lower normalized electron temperature gradient and a higher

Summary and discussion
Role of MTMs in pedestal transport is assessed in a DIII-D ELMy H-mode experiment with collisionality scan. As the pedestal-top electron collisionality is increased from 0.43 to 0.84, a drastic decrease in the pedestal electron temperature gradient is observed; whereas the pedestal electron density gradient is unchanged. Broadband (150-800 kHz) magnetic and density fluctuations, identified as originating from MTM instability, are measured. The fluctuation amplitudes increase at high collisionality and the density fluctuations peak in the pedestal gradient region, supporting the role of MTMs in limiting the pedestal temperature gradient. From low to high collisionality, experimentally-determined electron heat diffusivity increases ∼40% near the peak location of the density fluctuations whereas ion heat diffusivity is nearly changed, consistent with expected MTM-driven transport. Furthermore, a locally flattened region is observed in the electron temperature but not the density pedestal at high collisionality, a perhaps identifying feature of MTM-dominated transport as predicted by a global nonlinear simulation [7]. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, a set of local, nonlinear gyrokinetic simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. The comprehensive set of evidence presented herein strongly supports that MTMs dominate pedestal electron heat transport, in particular at the high collisionality. This work does not necessarily rule out the potential role of Electron-Temperature-Gradient mode, which has also been predicted unstable in H-mode pedestal [5], and is at a much higher wavenumber range than fluctuations investigated here. MTMs are expected to mainly affect electron heat transport [7]; other instabilities, which might correspond to the observed fluctuations below 150 kHz (figure 3), would be necessary to explain transport in the other channels. This result has several important implications. First, MTM instability should be included as an essential element in pedestal physics model. Although MTMs might not dominate in future fusion devices, which will have a lower collisionality than present machines; it will be important to verify in simulation and future experiment. Second, MTMs appear to have no direct effect in limiting the final pedestal pressure gradient in the ELM cycle: the density (and therefore the pressure) gradient keeps growing after the temperature gradient is clamped by MTMs ( figure 5). The final pedestal pressure gradient before ELM appears to be limited by other instabilities. However, MTMs might affect the final pressure pedestal indirectly: the reduced temperature gradient results in lower pedestal electron temperature and therefore higher pedestal collisionality, which could trigger ELM earlier at a lower pedestal pressure [38], consistent with the higher ELM repetition frequency at high collisionality ( figure 2). Lastly, the pedestal-top pressure in the investigated discharge decreases at higher electron density (figure 3(e)); this has long been known as the H-mode confinement degradation at high density [39]. The finding of MTM-dominated electron heat transport makes MTM a potential mechanism contributing to this degradation.